Geometry Honors Course 1206320

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Geometry Honors

(High School
)

Course
12
06320

Year at a Glance

Holt McDougal

Larson Geometry


Page
1

REV
11/08/12

Course description:

http://www.floridastandards.org/Courses/Pu
blicPreviewCourse37.aspx


NG
SSS:

http://www.floridastandards.org/Standards/FLStandardSearch.aspx



Throughout the year, students will relate new vocabulary to familiar words, listen to, read, and discuss familiar and concept
ually challenging text and will use new
vocabulary that is introduced and taught directly. (LA.910.1.6.1,

6.2, 6.5

and LA.1112.1.6.
1, 6.2, 6.5
)

Students will also use a variety of problem solving
strategies and will apply these skills using axioms and theorems in writing proofs.

(MA.912.
G.8.1 through 8.6
)



First Quarter

Second

Quarter


Chapter 1

Body of Knowledge: Geometry

Standard
1: Points, Lines, Angles, and
Planes

MA.912.G.1.1

MA.912.G.2.1,

2.7

Building Blocks of Geometry

A.

Defining point, line, angle, ray, plane

B.

Segments and their measures

C.

Angles and their measures

D.

Segment and
a
ngle bisectors

E.

Introduction to
p
erimeter,
circumf
erence
and
a
rea




Chapter 2

Body of Knowledge: Discrete
Mathematics

Standard 6:
Logic

MA.912.D.6.1,

6.2, 6.4

Body of Knowledge: Geometry

Standard 4: Triangles

MA.912.G.4.5

Standard 8: Mathematical Reasoning
and Problem Solving

MA.912.G.8.1

through 8.6

(on
-
going)



Reasoning and Proof In Geometry

A.

Inductive reasoning

B.

Deductive reasoning

C.

Conditional statements

D.

Reasoning with properties of Algebra

E.

Proving theorems

F.

Planning a proof




Chapter 3

Body of Knowledge: Geometry

Standard 1: Points, Lines,
Angles, and
Planes

MA.912.G.1.2, 1.3

Perpendicular and Parallel Lines

A.

Lines and angles

B.

Parallel and transversals

C.

Proving lines and parallel

D.

Lines in the coordinate plane



Chapter 4

Body of Knowledge: Geometry

Standard 2: Polygons

MA.912.G.2.2, 2.6

Stand
ard 4: Triangles

MA.912.G.4.1, 4.3

Congruent Triangles

A.

Triangles and angles

B.

Triangle inequality

C.

Proving triangles are congruent

D.

Applications in the real
-
world





Chapters 5 and 6

Body of Knowledge: Discrete
Mathematics

Standard 6: Logic

MA.912.D.6.3,

6.4

Body of Knowledge: Geometry

Standard 1: Points, Lines, Angles, and
Planes

MA.912.G.1.2





Standard 4: Triangles

MA.912.G.
2.3,
4.2,4.3, 4.4, 4.6, 4.7

Properties of triangles

A.

Medians, altitudes midsegment

B.

Perpendiculars and bisectors

C.

Inequalities in
triangles

D.

Construction of angles

E.

Inequality theorems


Similarity


A. Use properties of similar triangles


B. Apply segment divided proportionally


theorems


C. Prove triangles are similar


Body of Knowledge: Geometry

Standard 2: Polygons

MA.912.G.2.4, 2.6

Transformations

A.

Transformations

B.

Reflections

C.

Rotations

D.

Translations






Geometry Honors

(High School
)

Course
12
06320

Year at a Glance

Holt McDougal

Larson Geometry


Page
2

REV
11/08/12

Course description:

http://www.floridastandards.org/Courses/Pu
blicPreviewCourse37.aspx


NG
SSS:

http://www.floridastandards.org/Standards/FLStandardSearch.aspx



Third Quarter

Fourth Quarter


Chapter 7

Body of Knowledge: Geometry

Standard 5: Right Triangle

MA.912.G.5.1 through 5.4

Body of Knowledge: Trigonometry

Standard 2:

Trigonometry of Triangles

MA.912.T.2.1

Right Triangles & Trigonometry

A.

Pythagorean theorem and converse

B.

Special right triangles

C.

Similarity in right triangles

D.

Right triangle trig ratios

E.

Law of sines and cosines

F.

Solve real
-
world problems using
trigonometry



Chapter 8

Body of Knowledge: Discrete
Mathematics

Standard 6: Logic

MA.912.D.6.2, 6.4

Standard 11: Sequences and Series

MA.912D.11.5

Body of Knowledge: Geometry

Standard 2: Polygons

MA.912.G.2.3, 2.5

Standard 3: Quadrilaterals

MA.912.G.3.1 through
3.4





Quadrilaterals

A.

Polygons

B.

Properties of parallelograms

C.

Proving quadrilaterals are
parallelograms

D.

Rhombuses, rectangles and squares

E.

Trapezoids and kites

F.

Proving theorems about
quadrilaterals

G.

Special quadrilaterals

H.

Fibonacci sequence and g
olden ratio
(Ch 6.3)

I.

Similarity (Ch 6.3)




Chapters 10 and 11

Body of Knowledge: Geometry

Standard 7: Polyhedra and Other
Solids

MA.912.G.7.4

Standard 6: Circles

MA.912.G.6.1 through 6. 7

Geometry of Circles

A.

Arc lengths and area of sectors

B.

Ratio of area
s

C.

Chord properties

D.

Tangent properties

E.

Arc and angle properties

F.

Circumference / diameter ratio

G.

Inscribed angles

H.

Area and circumference


Chapters 11 and 12

Body of Knowledge: Geometry

Standard 2: Polygons

MA.912.G.2.5

Standard 7: Polyhedra and other
Solids


MA.912.G.7.1, 7.2, 7.3, 7.5, 7.6, 7.7

Area and Volume

A.

Area of polygons

B.

Prisms and cylinders

C.

Pyramids and cones

D.

Displacement and density

E.

Spheres

F.

Polyhedrons

G.

Cross sections

H.

Total surface area

I.

Similar solids (Ch11.3)

.



Chapter 9

Body of Knowl
edge: Geometry


Standard 2: Polygons

MA.912.G.2.6

Standard 4: Triangles

MA.912.G.4.8


Body of Knowledge: Discrete
Mathematics


Standard 6: Logic

MA.912.D.6.4

Standard 9: Vectors

MA.912.D.9.3

Coordinate Geometry

A.

Vectors

B.

Midpoint formula(Ch 8)






Geometry Honors

(High School
)

Course
12
06320

Year at a Glance

Holt McDougal

Larson Geometry


Page
3

REV
11/08/12

Course description:

http://www.floridastandards.org/Courses/Pu
blicPreviewCourse37.aspx


NG
SSS:

http://www.floridastandards.org/Standards/FLStandardSearch.aspx



Qtr

1

Qtr 2

Qtr 3

Qtr 4

YEAR LONG

Text Alignment





MA.912.G.8.1

High

Analyze the structure of Euclidean geometry as an axiomatic system. Distinguish between undefined terms,
definitions, postulates, and theorems.






MA.912.G.8.2

Moderate

Use a variety o
f problem
-
solving strategies, such as drawing a diagram, making a chart, guess
-
and
-
check,
solving a simpler problem, writing an equation, and working backwards.






MA.912.G.8.3

Moderate

Determine whether a solution is reasonable in the context of the or
iginal situation.






MA.912.G.8.4

High

Make conjectures with justifications about geometric ideas. Distinguish between information that supports a
conjecture and the proof of a conjecture.






MA.912.G.8.5

High

Write geometric proofs, including proofs

by contradiction and proofs involving coordinate geometry. Use and
compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two
-
column, and
indirect proofs.






MA.912.G.8.6

High

Perform basic constructions using straighte
dge and compass, and/or drawing programs describing and
justifying the procedures used. Distinguish between sketching, constructing, and drawing geometric figures.


Week of Explicit
Instruction

Quarter 1

Text Alignment


MA.912.G.1.1

Moderate

Find the len
gths and midpoints of line segments in two
-
dimensional coordinate systems.



MA.912.G.1.2

Moderate

Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge
and compass or a drawing program, expla
ining and justifying the process used.



MA.912.G.1.3

Moderate

Identify and use the relationships between special pairs of angles formed by parallel lines and transversals.



MA.912.G.2.1

High

Identify and describe convex, concave, regular, and irregular

polygons.



MA.912.G.2.7

Moderate

Determine how changes in dimensions affect the perimeter and area of common geometric figures.



MA.912.D
.6.1

Moderate

Use truth tables to determine truth values of propositional statements.



MA.912.D.6.2

Modera
te

Find the converse, inverse, and contrapositive of a statement




MA.912.D.6.4

Moderate

Use methods of direct and indirect proof and determine whether a short proof is logically valid.



MA.912.G.4.5

Moderate

Apply theorems involving segments divided
proportionally.


Geometry Honors

(High School
)

Course
12
06320

Year at a Glance

Holt McDougal

Larson Geometry


Page
4

REV
11/08/12

Course description:

http://www.floridastandards.org/Courses/Pu
blicPreviewCourse37.aspx


NG
SSS:

http://www.floridastandards.org/Standards/FLStandardSearch.aspx



Week of Explicit
Instruction

Quarter 2

Text Alignment


MA.912.G.2.2

Moderate

Determine the measures of interior and exterior angles of polygons, justifying the method used.



MA.912.G.2.
6

High

Use coordinate geometry to prove properties

of congruent, regular and similar polygons, and to perform
transformations in the plane.



MA.912.G.4.1

Moderate

Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and
equiangular.



MA.912.
G.4.3

High

Construct triangles congruent to given triangles.



MA.912.D.6.3

Moderate

Determine whether two propositions are logically equivalent.



MA.912.D.6.4

Moderate

Use methods of direct and indirect proof and determine whether a short proof is log
ically valid.



MA.912.G.1.2

Moderate

Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge
and compass or a drawing program, explaining and justifying the process used.



MA.912.G.2.3


High

Use properties of congruent and similar polygons to solve mathematical or real
-
world problems.



MA.912.G.4.2

Moderate

Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors,orthocenter, centroid,
incenter, and circum
center.



MA.912.G.4.3

High

Construct triangles congruent to given triangles.



MA.912.G.4.4

Moderate

Use properties of congruent and similar triangles to solve problems involving lengths and areas.



MA.912.G.4.6

High

Prove that triangles are congruent

or similar and use the concept of corresponding parts of congruent triangles.



MA.912.G.4.7

Moderate

Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge theorem.



MA.912.G.2.4

High

Apply transformations (tran
slations, reflections, rotations, dilations, and scale factors) to polygons. to determine
congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are
congruent to the original shape. Create and verify tesse
llations of the plane using polygons.



MA.912.G.2.
6

High

Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform
transformations in the plane.


Geometry Honors

(High School
)

Course
12
06320

Year at a Glance

Holt McDougal

Larson Geometry


Page
5

REV
11/08/12

Course description:

http://www.floridastandards.org/Courses/Pu
blicPreviewCourse37.aspx


NG
SSS:

http://www.floridastandards.org/Standards/FLStandardSearch.aspx



Week of Explicit
Instruction

Quarter 3

Text Alignment



MA.912.G.5.1

High

Prove and apply the Pythagorean
theorem

and its
co
nverse
.







MA.912.G.5.2

Moderate

State and apply the relationships that exist when the
altitude

is drawn to the
hypotenuse

of a
right triangle
.







MA.912.G.5.3

Moderate

Use special
right triangles

(30°
-

60°
-

90° and 45°
-

45°
-

90°) to solve problems.






MA.912.G.5.4


High

Solve real
-
world problems involving right triangles.



MA.912.T.2.1

Moderate

Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right
triangles.



MA.912.D.6.3

Moderate

Determine whether two propositions are logically equivalent.



MA.912.D.6.4

Moderate

Use methods of direct and indirect proof and determine whether a short proof is logically valid.



MA.912.D.11.5

High

Explore and use other
sequences

found in nature such as the
fibonacci sequence

and the
golden ratio
.






MA.912.G.2.3


High

Use properties of congruent and similar polygons to solve
mathematical or real
-
world problems.



MA.912.G.2.5

Moderate

Explain the derivation and apply
form
ulas

for
perimeter

and
area

of
polygons

(triangles,
quadrilaterals
,
pentagons
,
etc.).






MA.912.G.3.1

Moderate

Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus,
paralle
logram, trapezoid, and kite.



MA.912.G.3.2

Moderate

Compare and contrast special quadrilaterals on the basis of their properties.



MA.912.G.3.3

High

Use coordinate geometry to prove properties of congruent, regular, and similar quadrilaterals.



MA.91
2.G.3.4

High

Prove theorems involving quadrilaterals.



MA.912.G.7.4

Low

Identify chords, tangents, radii, and great circles of spheres




MA.912.G.6.1

High

Determine the center of a given
circle
. Given three
points

not on a
line
, construct the
circle

that passes t
hrough them.
Construct tangents to
circles
. Circumscribe and inscribe
circles

about and within
triangles

and regular
polygons
.






MA.912.G.6.2


Low

Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric
circles.


Geometry Honors

(High School
)

Course
12
06320

Year at a Glance

Holt McDougal

Larson Geometry


Page
6

REV
11/08/12

Course description:

http://www.floridastandards.org/Courses/Pu
blicPreviewCourse37.aspx


NG
SSS:

http://www.floridastandards.org/Standards/FLStandardSearch.aspx




MA.912.G.6.4

Moderate

Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and
tangents).



MA.912.G.6.5

High

Solve real
-
world problems using measures of circumference, arc length, and areas o
f circles and sectors.



MA.912.G.6.6

Moderate

Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in
center
-
radius form, state the center and the radius of the circle.



MA.912.G
.6.7

Moderate

Given the equation of a circle in center
-
radius form or given the center and the radius of a circle, sketch the graph of
the circle.


Geometry Honors

(High School
)

Course
12
06320

Year at a Glance

Holt McDougal

Larson Geometry


Page
7

REV
11/08/12

Course description:

http://www.floridastandards.org/Courses/Pu
blicPreviewCourse37.aspx


NG
SSS:

http://www.floridastandards.org/Standards/FLStandardSearch.aspx



Week of Explicit
Instruction

Quarter 4

Text Alignment


MA.912.G.2.5

Moderate

Explain the derivation and apply
formulas

for
perimeter

and
area

of
polygons

(triangles,
quadrilaterals
,
pentagons
,
etc.).






MA.912.G.7.1

Moderate

Describe and make regular, non
-
regular, and oblique polyhedra, and sketch the net for a given polyhedron and vice
versa.



MA.912.G.7.2

Moderate

Describe the relationships between the
faces
,
edges
, and
vertices

of polyhedra.




MA.912.G.7.3

Mo
derate

Identify, sketch, find areas and/or
perimeters

of cross sections of solid objects.






MA.912.G.7.5

Moderate

Explain and use formulas for lateral area, surface area, and volume of solids.



MA.912.G.7.6

Moderate

Identify and use properties of congruent and similar solids.



MA.912.G.7.7

Moderate

Determine how changes in dimensions aff
ect the surface area and volume of common geometric solids.



MA.912.G.2.
6

High

Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform
transformations in the plane.




MA.912.G.4.8

High

Use
coordinate

geometry

to prove properties of
congruent
, regular, and similar
triangles
.






MA.912.D.6.4

Moderate

Use methods of direct and indirect proof and determine whether a short proof is logically valid.




MA.912.D.9.3

High

Use
vecto
rs

to
model

and solve application problems.